Question: Solve for $x$ and $y$ using elimination. ${-6x-3y = -39}$ ${5x+4y = 40}$
Explanation: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $5$ and the bottom equation by $6$ ${-30x-15y = -195}$ $30x+24y = 240$ Add the top and bottom equations together. $9y = 45$ $\dfrac{9y}{{9}} = \dfrac{45}{{9}}$ ${y = 5}$ Now that you know ${y = 5}$ , plug it back into $\thinspace {-6x-3y = -39}\thinspace$ to find $x$ ${-6x - 3}{(5)}{= -39}$ $-6x-15 = -39$ $-6x-15{+15} = -39{+15}$ $-6x = -24$ $\dfrac{-6x}{{-6}} = \dfrac{-24}{{-6}}$ ${x = 4}$ You can also plug ${y = 5}$ into $\thinspace {5x+4y = 40}\thinspace$ and get the same answer for $x$ : ${5x + 4}{(5)}{= 40}$ ${x = 4}$